The longer the acceleration, the greater the change in velocity. The relation between velocity and time is a simple one during uniformly accelerated, straight-line motion. As long as you are consistent within a problem, it doesn't matter. Some problems are easier to understand and solve, however, when one direction is chosen positive over another. The laws of physics are isotropic that is, they are independent of the orientation of the coordinate system. Determining which direction is positive and which is negative is entirely arbitrary. Since we are dealing with motion in a straight line, direction will be indicated by sign - positive quantities point one way, while negative quantities point the opposite way. In this order, they are also often called the first, second, and third equations of motion, but there is no compelling reason to learn these names. There are three ways to pair them up: velocity-time, position-time, and velocity-position. Our goal in this section then, is to derive new equations that can be used to describe the motion of an object in terms of its three kinematic variables: velocity ( v), position ( s), and time ( t). It is such a useful technique that we will use it over and over again. This is the way things get done in physics. Approximating real situations with models based on ideal situations is not considered cheating. (You can't drive diagonally on a road and hope to stay on it for long.) In this regard, it is not unlike motion restricted to a straight line. A road might twist and turn and explore all sorts of directions, but the cars driving on it have only one degree of freedom - the freedom to drive in one direction or the opposite direction. Motion along a curved path may be considered effectively one-dimensional if there is only one degree of freedom for the objects involved. So what good is this section then? Well, in many instances, it is useful to assume that an object did or will travel along a path that is essentially straight and with an acceleration that is nearly constant that is, any deviation from the ideal motion can be essentially ignored. This I can say with absolute metaphysical certainty. It would be correct to say that no object has ever traveled in a straight line with a constant acceleration anywhere in the universe at any time - not today, not yesterday, not tomorrow, not five billion years ago, not thirty billion years in the future, never.

Given that we live in a three dimensional universe in which the only constant is change, you may be tempted to dismiss this section outright.

These equations of motion are valid only when acceleration is constant and motion is constrained to a straight line. Given that such a title would be a stylistic nightmare, let me begin this section with the following qualification. For the sake of accuracy, this section should be entitled 'One dimensional equations of motion for constant acceleration'.

Law of motion